[tbworld]

As @Lynne was saying, you need a php widget.

Create a new widget template and insert the following:

<!-- 2014_07_16__php_search_widget -->
<style>
.tb_widget_content {
  background: #203020;
}
.tb_button {
  width: 24px;
  vertical-align: middle;
}
.tb_textbox {
  background: #A7B7A7;
  color: black;
  border: 0 none;
  height: 24px;
  width: 240px;
  font-size: 13px;
 } 
.tb_advanced_search li a {
  color: white;
}
</style>

<div class="cms_widget">
<div class="block">
<div class="cms_widget_header widget_header">
    <h3><img src="{vb:stylevar imgdir_siteicons}/php.png" alt="" /> {vb:raw title}</h3>
</div>
<div class="cms_widget_content widget_content tb_widget_content">


    <form action="search.php?{vb:raw session.sessionurl}do=process" method="post" id="tb_search" class="tb_search">
        <input type="hidden" name="securitytoken" value="{vb:raw bbuserinfo.securitytoken}" />
        <input type="hidden" name="do" value="process" />
        
        <span>
            <input type="text"  class="tb_textbox textbox" value="" name="query" tabindex="99"/>
            <input type="image" class="tb_button" src="{vb:stylevar imgdir_button}/search.png" name="submit" onclick="document.getElementById('tb_search').submit;" tabindex="100"/>
        </span>
    </form>
    
    <!-- Advanced Search -->
    <ul class="tb_advanced_search">
        <li><a href="search.php{vb:raw session.sessionurl_q}" accesskey="4">{vb:rawphrase advanced_search}</a></li>
    </ul>


</div>
</div>
</div>

Notes
---------------
1.) This uses a php widget, but is not inserting any new php -- all variables that we are using are already registered in the normal vbulletin context. You should be trying this under the vbulletin default style.

2.) This is not inserted into the widget configuration. This code is added to a newly created template (Template Manager). Use the name of the template (case sensitive) and replace the template name in the widget configuration textbox (at the bottom of the widget configuration page).